The 2-Space Offset Problem
I have a 1.5L Hydration Progress graph that is basically a grid of check-boxes that I can tick for each 10mL increment I have accomplished for the day, typically by drinking 100mL in one drink, meaning I can tick 10 boxes. The percentage adds up no matter what order you tick the boxes, meaning you can skip around randomly in the graph and the raw number of boxes ticked contributes to the total. I mix up the ways I tick boxes sometimes, and today was a new way. The grid is 5 boxes tall by 20 boxes wide, 20% per row.
Today (2026-0324) I opted to tick the boxes off by making an L-shape. Starting at the upper left, I ticked the first box in each row, followed by the remaining 5 boxes along the bottom row going right, for 10%.
| x | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o |
| x | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o |
| x | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o |
| x | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o |
| x | x | x | x | x | x | o | o | o | o | o | o | o | o | o | o | o | o | o |
The next 10% increment, I made another L-shape, beginning with the 2nd box of row 1, going down, and to the right with the remainder, so 4 down and 6 over.
| x | x | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o |
| x | x | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o |
| x | x | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o |
| x | x | x | x | x | x | x | x | o | o | o | o | o | o | o | o | o | o | o |
| x | x | x | x | x | x | o | o | o | o | o | o | o | o | o | o | o | o | o |
I noticed that although I was going “over” only 1 more box more, the tip of the next-to-last-row was 2 spaces further than the bottom one.
Next 10% increment, it extended another 2 boxes further, even though the line only increased by 1 again.
| x | x | x | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o |
| x | x | x | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o | o |
| x | x | x | x | x | x | x | x | x | x | o | o | o | o | o | o | o | o | o |
| x | x | x | x | x | x | x | x | o | o | o | o | o | o | o | o | o | o | o |
| x | x | x | x | x | x | o | o | o | o | o | o | o | o | o | o | o | o | o |
The answer seems really obvious to me now, but it wasn't until I plotted these out that I realized why it was 2 longer, despite only increasing by 1 per row.
As simple as it may be for me, I wonder what the youngest a person could be to solve this problem.